Long Answer Questions
1. [3 marks] An educational researcher wants to evaluate the effectiveness of a new method for teaching
reading to deaf students. Achievement at the end of a period of teaching is measured by a student’s
letter grade (A+, A, A-, B+, etc.) obtained on a reading test.
A. [1] What is the variable of interest to be measured?
B. [1] What type of variable is it (i.e. quantitative discrete, quantitative continuous or
qualitative/categorical)?
C. [1] What is the experimental unit?
2. [11 marks] The midterm grades (𝑥) and final grades (𝑦) of 250 students were recorded. Both grades
are out of 100. They are summarized in the following table
∑ 𝑥𝑖
∑ 𝑦𝑖
∑ 𝑥𝑖2
∑ 𝑦𝑖2
∑ 𝑥𝑖 𝑦𝑖
15065 14842.5 962357.9 909494.5 933556.8
A. [6] Compute the value of the correlation coefficient between 𝑥 and 𝑦. I.e., compute 𝑟.
B. [4] Find the equation of the regression line with midterm grade as independent variable (the predictor)
and the final grade as dependent variable (response).
C. [1] The midterm grades (𝑋) range from 5 to 99. Predict the final grade of a student who received 80 on
their midterm.
3. [14 marks] The data below are the days 15 students waited until they heard the result from their
COVID-19 test.
1.1, 1.4, 1.5, 1.5, 1.8, 1.9, 2, 2.1, 2.4, 2.5, 2.8, 3, 3, 4.1, 7
A. [6] Calculate the mean, range, variance and standard deviation for these data.
B. [5] Construct the boxplot for these data. Use your boxplot to determine if the distribution is symmetric
(or mound shape). Explain your answer.
C. [3] The value X = 7 appears to be an outlier. Use a Z-score to decide whether this is an unusually long
time to wait.
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4. [8 marks] 60 % of students who apply to do a masters in statistics have an undergraduate degree in
statistics, 25% have an undergraduate degree in mathematics, and 15% an undergraduate degree is a
program other than statistics or mathematics. The acceptance percentage is 85%, 75%, and 60% for
statistics, mathematics, and other degree respectively.
A. [1.5] If an applicant is randomly selected, what is the probability he/she has a degree in mathematics
and got accepted?
B. [2.5] If an applicant is randomly selected, what is the probability he/she didn’t get accepted?
C. [4] If an applicant is randomly selected and was found to be accepted, what is the probability he/she
has an undergraduate degree from a program other than mathematics or statistics?
5. [10 marks] A contractor is interested in the total cost of a project on which he intends to bid. He
knows that his costs will be $600 per day (for labour), plus a fixed cost of $15,000 (for materials, etc.).
The contractor forms subjective probability assessments of the number of days, Y , that will be
required to complete the project as shown below:
Y
p(y)
1
0.1
2
0.3
3
0.3
4
0.2
A. [2] Find the expected number of days needed to complete the project, Y .
B. [2] Find the variance of the completion time, Y .
C. [3] What is the expected value of the total cost of the project?
D. [3] What is the standard deviation of the total cost?
Multiple Choice Question
1. The diameters (in inches) of 30 cherry tress are recorded. The values are summarized in the
following stem- and-leaf graph
8 | 368
10 | 57800123447
12 | 099378
14 | 025
16 | 0335
18 | 00
20 | 6
Leaf unit=0.1
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5
0.1
Which one of the following statements is correct?
A. Mean > Median
B. Median > Mean
C. The Mean and Median are approximately equal
D. Median is closer to the upper quartile
E. Upper quartile is located between the 25th and 26th measurements
2. The waiting time (in minutes) for 272 eruptions of Old Faithful which is a geyser in Yellowstone
National Park were recorded. The histogram of the data is left or negatively skewed. The mean and
standard deviation of the data set respectively are 𝑋̅ = 71 𝑚𝑖𝑛𝑢𝑡𝑒𝑠, 𝑆 = 13.6 𝑚𝑖𝑛𝑢𝑡𝑒𝑠. How many
of the 272 eruptions are between 44.68 minutes and 97.32 minutes?
A. Approximately 258
B. Approximately 181
C. At least 270
D. At least 204
E. At least 242
3. Consider the following incomplete probability distribution of the random variable X.
x
P(X=x)
1
???
2
???
3
0.05
4
0.30
5
0.25
P(X ≤ 3) is
A. 0.60
B. 0.40
C. 0.45
D. 0.55
E. Can’t be determined
4. A hiring committee of 3 members is to be selected. If there are 30 people to select from, how many
committees are possible?
A. 4060
B. 24360
C. 90
D. 24360
E. 27000
5. Let A and B be two events defined on the same sample space. If P(A) = 0.4, P(B) = 0.5, and P(B|A) =0.1.
Then P(AUB) is
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A. 0.80
B. 0.90
C. 0.20
D. 0.86
E. 1.00
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